Answer:
If you receive a 15% discount on a shirt that normally costs £42, the discounted price of the shirt will be £42 - (15/100) * £42 = £35.70. If you pay £50 for the shirt, you will receive £50 - £35.70 = £14.30 in change. Therefore, the correct answer is D- £14.30.
Step-by-step explanation:
Can someone solve this and show the work?
The length of the side a is 112.1664 cm.
What is Law of sines?The ratios of a triangle's side lengths to each of its opposite angles are related by the law of sines. There is no change in this ratio for the three sides or the opposing angles.
The Law of sines;
Sin A / a = Sin B / b = Sin C/ c
Here, we have two angles 35° and 25° and a side b = 5 ft
Now, sin35°/5 = sin25°/a
a = (0.42) x 5 / (0.57)
a = 3.68
Now the length in feet is 3.68 cm.
Therefore, the length of the side a is 112.1664 cm.
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Men's heights are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches, while women's heights are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches.
(a) What percentage of men must duck when walking through a door that is 72 inches high?
(b) What percentage of women must duck when walking through a door that is 70 inches high?
(c) What door height would allow at least 95% of men to walk through the door without ducking?
Approximately 95% of men must duck when walking through a door that is 72 inches high. Approximately 5% of women must duck when walking through the door. The door height that would allow at least 95% of men to walk through the door without ducking is 74 inches.
The mean height of men is 69.0 inches and the standard deviation is 2.8 inches, while the mean height of women is 63.6 inches and the standard deviation is 2.5 inches.
(a) To find the percentage of men who must duck when walking through a door that is 72 inches high, we first need to find the percentage of men whose height is less than 72 inches.
The height of the door is 72 inches, which is 3 inches above the mean height of men.
Since the standard deviation is 2.8 inches, this means that approximately 95% of men are within 2.8 * 2 = 5.6 inches of the mean height.
Therefore, approximately 95% of men are between 69.0 - 5.6 = 63.4 inches and 69.0 + 5.6 = 74.6 inches tall.
If the height of the door is 72 inches, approximately 95% of men must duck when walking through the door.
(b) To find the percentage of women who must duck when walking through a door that is 70 inches high, we first need to find the percentage of women whose height is less than 70 inches.
The height of the door is 70 inches, which is 6.4 inches above the mean height of women.
Since the standard deviation is 2.5 inches, this means that approximately 95% of women are within 2.5 * 2 = 5 inches of the mean height. Therefore, approximately 95% of women are between 63.6 - 5 = 58.6 inches and 63.6 + 5 = 68.6 inches tall.
If the height of the door is 70 inches, approximately 5% of women must duck when walking through the door.
(c) To find the door height that would allow at least 95% of men to walk through the door without ducking, we need to find the height that is within 2 standard deviations of the mean height of men.
Since the standard deviation is 2.8 inches, this means that approximately 95% of men are within 2.8 * 2 = 5.6 inches of the mean height.
Therefore, the door height that would allow at least 95% of men to walk through the door without ducking is 69.0 + 5.6 = 74
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PLEASE HELP 50 Points + award.
Answer: 2nd first 1st second third 4th fourth 3rd and 5th in 5th
Step-by-step explanation:
For the regions A and B shown in the graph:
Part A: Discuss the limits of integration.
Part B: Set up an integral expression that represents the total area.
Part C: Calculate the total area.
The area for the shaded region is obtained as 2 units.
How to find the area between two curves?In order to find the area, first find the intersection points of the two curves. Then, the area of the region can be found by taking the integration from the intersection point.
The curves in the graph in the form of equation are as follows,
y = x² + 3 (1)
x = (y - 5)² - 2
=> y = √(x+ 2) + 5 (2)
Part A :
The intersection points of the two curves are (-1.5, 5.5), (-1, 4) and (0.5, 3.5).
Thus, to calculate the area the limit is from x = -1.5 to x = 0.5.
Part B :
The expression of the integral is given as,
[tex]\int\limits^{-1}_{-1.5} {(x^{2} + 3 ) - (5 + \sqrt{x + 2} )} \, dx + \int\limits^{0.5}_{-1} {(5 + \sqrt{x + 2} ) -(x^{2} + 3 ) } \, dx[/tex]
Part C :
The area is found by evaluating the integral as follows,
[tex]\int\limits^{-1}_{-1.5} {(x^{2} + 3 ) - (5 + \sqrt{x + 2} )} \, dx + \int\limits^{0.5}_{-1} {(5 + \sqrt{x + 2} ) -(x^{2} + 3 ) } \, dx[/tex]
= [-1/3 + 3.375/3 + 3(-1 - (-1.5))] - [5(-1 - (-1.5)) + 2/3([tex]1^{3/2} - 0.5^{3/2}[/tex])] + [5(0.5 - (-1)) -(0.125/3 + 1/3 + 3(0.5 - (-1))]
= 2.291 - [2.5 + 2/3 × 0.647] + [5 × 1.5 - 4.8716]
= 2.291 - 2.927 + 2.6284
= 1.9924
Which is approximately 2.
Hence, the area between the curves is given as 2 units.
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Jennifer has 76 inches of string to make bracelets. She uses 8 inches for each bracelet. How many bracelets can she make?
I got it wrong again >:(
As a consumer starts paying his loan, the interest tends to decrease.
A. True
B. False
Answer:
A. true
Step-by-step explanation:
I believe you pay most of your interest when you first receive the loan.
Multiply the complex numbers: (1∕2 + 4i)2
Question 18 options:
A) –153∕4 + 8i
B) 153∕4 + 4i
C) 153∕4 + 8i
D) –153∕4 + 4i
Since -153/4 + 4i is equivalent to -63/4 + 4i, we should multiply D) –153∕4 + 4i to complex numbers (1∕2 + 4i)².
Define complex numbers.Complex numbers are those that are expressed as a+ib, where a and b are actual numbers and I is a fictitious number called a "iota." I has the value (-1). As an illustration, the complex number 2+3i is made up of the real number 2 (Re) and the imaginary number 3i (Im). In the case of quadratic equations, the unknown roots are simplified using complex numbers if the roots are not real. In computer science and engineering, complex numbers are used. Both mechanical and civil engineering use complex numbers. Control systems employ complex numbers.
Given,
Complex numbers:;
(1/2 + 4i)²
(a +b )² = a² + b² + 2ab
Multiplying,
(1/2)² + (4i)² + 2(1/2)(4i)
1/4 + 16i² + 4i
i² = -1
1 - 64/4 + 4i
-63/4 + 4i
Since -153/4 + 4i is equivalent to -63/4 + 4i, we should multiply D) –153∕4 + 4i to (1∕2 + 4i)².
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Solve equation
176 =-4(4 + 6m)
to solve for m
distribute into parentheses
176 = -16 - 24m
get m on one side
176 + 16 = -24m
192 = -24m
divide by -24
-8 = m
m = -8
HEEEEEEEP
(b) A certain arcade game gives players tickets. The table below shows the
number of tickets a player gets for the number of points.
Tickets
Points
32
4
56
8
CO
63
9
O Each point does not always give the same number of tickets.
Each point appears to give the same numb of tickets.
Predicted number of tickets for getting 10 point:
Answer:
Step-by-step explanation: Can u show the picture of the table so i can understand this better
A certain model of a solar panel produces 1,200 KW of power for an area of one square meter,2,400 KW of power for an area of two square meters,and 3,600 KW of power for three square meters. Determine if the amount of power y the solar panel can produce is proportional to the size of x.Then graph.
The amount of power y the solar panel can produce is linearly proportional to the size of x, the equation is y = 1200x, and the graph is attached below.
What is a graph?A graph is a structure made up of a collection of things, where some object pairs are conceptually "connected." The items are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.
Given data:
A certain model of a solar panel produces 1,200 KW of power for an area of one square meter,2,400 KW of power for an area of two square meters, and 3,600 KW of power for three square meters,
As you can see from the above, the power is linearly dependent on the area, and it can be seen by the following equation,
y = 1200x
Here, y = power and x = area,
Therefore, the amount of power y the solar panel can produce is linearly proportional to the size of x, the equation is y = 1200x, and the graph is attached below.
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Colleen is searching online for airline tickets.Two weeks ago, the cost to fly. The from Boston to Orlando was $225.Now the cost is $355. What is the percent increase? What would be the percent increase if the airline charges an additional $50 Baggage fee with the new ticket price?
Answer:
15
Step-by-step explanation:
Which one is it?? Pls helpppp
Answer:
6x-3=15
Step-by-step explanation:
Draw a line representing the "rise" and a line representing the "run" of the line. State
the slope of the line in simplest form.
The slope of the line in the graph is 2/3.
What is a slope?In general, the slope of a line indicates its steepness and direction. The slope of a straight line between two points, say (x1,y1) and (x2,y2), can be easily calculated by subtracting the coordinates of the points. The letter 'm' is commonly used to represent the slope.A line's slope is defined as
Slope = Rise / Run
Can also be written as,
slope(m) = y2 - y1 / x2 - x1
Choose any two points on the line, such as A and B.
It is clear from the graph below that
Rise = y Change = -3-(-1) = -2
Run = x Change = 1 - 4 = -3
In the above formula, substitute these values.
Slope = -2 / -3
= 2/3
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What property is 13(20x5)
Answer: The distributive property
Step-by-step explanation: The distributive property ALWAYS has 1 number that is outside the parentheses. I know you didn't ask for this, but you can use the distributive property to write an equivalent expression by multiplying (or distributing) the 13 by every # inside the parentheses, so your new equation would look like 260 x 65. I hoped this explanation and example help you understand now.
find the value of a + 4 when a = 13
Answer:
17
Step-by-step explanation:
13 + 4 = 17
RADICAL FUNCTIONS PROBLEM PLS HELP!!!!
Answer:
-4
Step-by-step explanation:
So we have f(x) = x + 1 and g(x) = 5x. We need to find f(g(x))(-1). So let's put g(x) into f(x): f(g(x)) = f(5x) = 5x + 1. Now we have x = -1. Let's substitute this into 5x + 1 = -5 + 1 = -4.
PLS HELP IM GETTING ABUSED ): 50 POINTS
These items are all on sale with one-third off. What was the full price of each?
Sale price: Original full price:
£32.24 £_________
£86.08 £_________
£105.48 £_________
£230.62 £___________
The full price when the sales price is ;
£32.24 = £96.72
£86.08 is £258.24
£105.48 is £316.44
£230.62 is £691.86
What are the full prices?The sales price is one third of the full price of the items. Thus, in order to determine the full price, multiply the sales price by 3.
Full price = sales price x 3
Full price when the sales price is £32.24 would be;
= 3 x £32.24
= £96.72
Full price when the sales price is £86.08 would be;
= 3 x £86.08 = £258.24
Full price when the sales price is £105.48 would be;
= 3 x £105.48 = £316.44
Full price when the sales price is £230.62 would be;
= 3 x £230.62 = £691.86
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Look at the equation below
y = 2x - 2
Which situation is best described by the situation?
a. The temperature at 2:00 am is 2 degrees celsius and rises 2 degrees each hour for x hours.
b. The temperature at 2:00 am is 2 degrees and rises 2 degrees each hour for x hours.
c. The temperature at 2:00 am is 2 degrees and drops 2 degrees each hour for x hours
d. The temperature at 2:00 am is -2 degrees celsius and drops 2 degrees each hour for x hours
The situation that is best described by the situation is that D. The temperature at 2:00 am is -2 degrees celsius and drops 2 degrees each hour for x hours.
Which situation is best described by the situation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
In this case, the equation is given as:
y = 2x - 2.
This illustrates that the temperature at 2:00 am is -2 degrees celsius and drops 2 degrees each hour for x hours.
In conclusion, the correct option is D.
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what is the value of h if h2=441?
Answer:
[tex]h=\pm 21[/tex]
Step-by-step explanation:
[tex]h^2=441 \implies h=\pm \sqrt{441}=\pm 21[/tex]
Jake had of a cake. He gave
6
2
4
of it to his friend at lunch. How
much more cake does Jake have
left?
Answer:
12 Pieces left!
Step-by-step explanation:
Because, Look. 6 is 1 quarter, He gave some of his other friends less.
If you add 2 + 4, thats 6! 6 is 1 quarter. There is 4 quarters in a cake. SO 6 + 6 12, thats half of a quarter. And then he gets the other half! Good luck!
(24 pieces in his cake)
i need hepl with all of this
The equivalent linear equation to the line 3x + 4y = 15 is the one in the first option:
y = (15 - 3x)/4
Which equation is equivalent to the given one?
Here we have the following linear equation:
3x + 4y = 15
And we want to find an equivalent linear equation where y is isolated in the left side of the equation. So let's isolate the variable.
If we subtract 3x in both sides of the linear equation we will get:
3x + 4y - 3x = 15 - 3x
4y = 15 - 3x
Now we can divide both sides by 4, so we will get:
4y/4 = (15 - 3x)/4
y = (15 - 3x)/4
This is the equation in option 1, so we conclude that the correct option is the first one.
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Determining the Value of an Unknown
What is the value of n in the equation --(2n + 4) + 6 = -9 + 4(2n + 1)?
The value of n in the given equation is 1.
Define Algebraic Expression
In mathematics, an expression that includes variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.)
Given equation,
-1/2 (2n + 4) + 6 = -9 + 4(2n + 1)
Now, solve for n
first, solve the brackets
-1/2 * 2n + (-1/2) * 4 + 6 = -9 + 4*2n + 4 * 1
-n - 2 + 6 = -9 + 8n + 4
Solve the constants on both the sides,
-n + 4 = 8n - 5
Now, take out n value one side and constant terms other side
-n - 8n = -5 - 4
-9n = -9
Cancel out -9 from both the sides,
n = 1
Hence, the value of n in the given equation is 1.
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Help me out with this question please
Answer:
148 cm²
Step-by-step explanation:
Using the formula for the total surface area of a cuboid,
[tex]2(6 \times 4+6 \times 5+4 \times 5)=148[/tex]
Please… help. Math modeling B
The strategic decision based on the p-value is given as follows:
Allow the machine to continue operating as it is.
How to make the decision?The decision depends if we reject or do not reject the null hypothesis in this problem, as follows:
Reject the null hypothesis: changes the operation of the machine.Do not reject the null hypothesis: allow the machine to continue operating as it is.The decision rule to accept or reject the null hypothesis is given as follows:
p-value greater than the significance level of 0.05 -> do not reject the null hypothesis.p-value less than the significance level of 0.05 -> reject the null hypothesis.The p-value in this problem is given as follows:
0.06811.
Which is greater than the significance level, hence the null hypothesis is not rejected and the first option is correct, as the machine should be allowed to continue operating as it is.
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Please help me on this I will give brainliest if possible
Answer:216
Step-by-step explanation:
Please help with this!!! Multiply 6x5 7/8
Answer:
35 and 1/4
Step-by-step explanation:
6x47/8
6/1x47/8
282/8
35 1/4 or 35.25
Find the sum of (5y−12)+(−5y−1).
Answer:
-13
Step-by-step explanation:
The ys can combine and so can the numbers so if you take -5y + 5y you get 0. so those completely cancel out, so then you would add -12 + -1 which is -13.
Can somebody help me on this? I thought I got it but then it didn’t turn out as I expected.
Answer: z=34 degrees
Step-by-step explanation:
the total angle of a triangle always adds up to 180
180=44+2z+2z
combine like terms
4z+44=180
4z+44-44=180-44
4z=136
z=34
find the z score that has 70.54% of the distribution area to its right
The z score that has 70.54% of the distribution area is 9.92
What is a z-score?The z-score is a numerical measurement used in statistics to refer to how much a given value differs from the standard deviation.
For the random variable x, the z-score is;
z = (x - 11)/2
therefore, 70.54% of the area under the curve lies to the right of x,
then the area to the left of x is;
100 - 70.54 = 29.46%
From the standard table, a z-score of -0.54 will yield an area of 29.46% to the left of x.
Therefore, we get;
(x - 11)/2 = -0.54
x - 11 = -0.54(2)
x = 9.92
The z score is 9.92
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